# The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic - Mathematics > Algebraic Geometry

The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic - Mathematics > Algebraic Geometry - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Let X be a general proper and smooth curve of genus 2 resp. of genus 3defined over an algebraically closed field of characteristic p. When 3\leq p\leq 7, the action of Frobenius on rank 2 semi-stable vector bundles withtrivial determinant is completely determined by its restrictions to the 30lines resp. the 126 Kummer surfaces that are invariant under the action ofsome order 2 line bundle over X. Those lines resp. those Kummer surfaces areclosely related to the elliptic curves resp. the abelian varieties ofdimension 2 that appear as the Prym varieties associated to double \-etalecoverings of X. We are therefore able to compute explicit equations of thisaction in these cases. We perform some of these computations and draw someconsequences.

Autor: Laurent Ducrohet

Fuente: https://arxiv.org/